This type of service was available in the UK from www.tvcatchup.com between about 12th Dec 07 and 16th Feb 08 but they were suddenly shut down by the broadcasters (The lawyers complained, and the admins shut down the site without a fight. However, after talks with the aforementioned lawyers, they have apparently reopened the service, although only to closed beta users for the time being).
Also, the average Joe does care about whether or not the storage is remote or local, because local storage has limited space before the user has to start deleting things. Remote storage has no theoretical limit (only artificial ones that can be changed any time, when the service provider adds HDDs). Plus, local storage has no bandwidth issues, whereas remote storage can have problems (My Dad would be considered an 'Average Joe', but we are unable to use BT Vision because we cannot receive Freeview in our part of London, and our BT Broadband is not stable enough to use the On Demand features and be able to guarantee a watchable service. The fact that the service would be free because my Dad works for BT is not enough incentive to use something that doesn't work).